4 - Moral Hazard Flashcards
What are the characteristics of a moral hazard situation?
- Principal (P) wants an agent (A) to perform a task
- only A knows the effort he exerts in the task -> postcontractual private information/moral hazard
- A can be risk neutral / protected by limited liability / risk averse
Which elements does a moral hazard problem contain?
- Principal (P) delegates a task to an agent (A)
- A exerts non‐observable effort e ∈ [0, 1] at cost c(e)
- Effort costs are increasing and strictly convex (c’>0, c’’(0)>0)
- We further assume that c’(0) = 0, c’’’ ≥ 0 (technical assumptions)
- Verifiable outcome of the task is either success (s=1) or failure (s=0)
- Probability of success is increasing in effort
- Pr[s=1|e] = e
- P’s payoff is S₀ in case of failure and S₁ in case of success, S₁ > S₀
- A’s reservation utility is u₀ ≥ 0
What are the conflicting interests in a typical moral hazard situation?
Conflicting interests of A and P: ceteris paribus, P prefers higher effort to increase the probability of a high payoff, whereas A prefers lower effort to save effort costs
How can principal & agent’s interests be aligned with a contract in a moral hazard situation? What would the contract specify?
- The contract cannot condition on e, but on s. The outcome of the task thus serves as a proxy for effort.
- The contract specifies A’s compensation t₀ and t₁ in case of failure and success, respectively.
- P is risk neutral and thus wishes to maximize his expected payoff net of A’s compensation. Initially, A is also risk neutral.
What is the timing of a moral hazard problem?
- P offers a contract specifying payments t₀ and t₁
- A accepts or refuses the contract
- A refuses -> A does not work for P and obtains his reservation utility
- A accepts -> stage 3
- A chooses effort e
- Outcome s is realized
- Contract is executed
What do we assume when calculating the first-best solution for a moral hazard problem?
that there was no asymmetric information = that e is verifiable
What does it mean to say that the participation constraint (PC) is binding?
Agent is compensated for his effort costs and opportunity costs but does not get anything more (no rent)
What is the expected result for a contract in a moral hazard situation with a risk-neutral agent?
Result: If the agent is risk neutral, the principal designs the contract such that the agent chooses the first‐best effort. Hence, even though there is a moral hazard problem, no efficiency loss occurs!
What does it mean if we apply “limited liability”?
- The payment to A needs to exceed a certain threshold L ∈ (-∞, ∞), i.e., t₀ ,t₁ ≥ L.
- This threshold is exogenously imposed.
Which three cases do we examplary consider for the values of L in real life?
Case 1:
- L = 0: A cannot make payments to P, e.g., because A has no wealth or due to legal restrictions
- P cannot punish the agent in case of failure (S0)
Case 2:
- L < 0: A can make payments to P but they cannot exceed –L, e.g., legal liability limit or A has restricted wealth or A is insured (e.g., firm owners can get only limited damages from top executives)
Case 3:
- L > 0: A has to obtain a positive base compensation (e.g., legal minimum wage)
What happens if The (LLC) is binding, but the (PC) is not?
Agent earns a rent.
How can we interpret a situation where LLC: L ≥ 0?
If the agent is risk neutral but his compensation needs to exceed a non‐negative threshold, the principal does not design the contract such that the agent chooses the first‐best effort. To keep the agent’s rent low, the principal distorts the agent’s incentives.
In other words: Because P is forced to pay a larger base compensation than without limited liability, he reduces A’s incentives.
What is a risk premium?
- The risk premium is the difference between the expected payoff of the lottery and the certainty equivalent.
- Risk premium = p t1 + (1‐p) t2 – CE ( > 0 under risk aversion)
- Intuition: For the individual to prefer a given lottery to a given certain payment x, the lottery‘s expected payoff needs to exceed x by (at least) the risk premium.
What effects does risk aversion have on a solution?
- Due to A’s risk aversion, inducing a given effort e is more expensive for P than if e was contractible.
- The parties’ joint surplus is lower than if e was observable.
- Risk aversion causes additional costs of incentive provision for the principal, leading to an efficiency loss relative to the first‐best solution.
When do postcontractual private information lead to an efficiency loss?
- If there is an exogenously imposed wage floor (limited liability)
- If A is risk averse
